Wave-equation tomography using image-space phase-encoded data

introduction

Wave-equation tomography has the potential to overcome the problems faced by ray-based traveltime tomography when estimating the velocity model in complex geological scenarios. This is because wave-equation tomography uses band-limited wavefields instead of infinite-frequency rays as carriers of information; thus it is robust even in the presence of strong velocity contrasts and immune to multi-pathing issues. However, despite its theoretical advantages, wave-equation tomography is still computationally challenging.

Wave-equation tomography can be performed in the data-space domain (Woodward, 1992; Tarantola, 1987) or in the image-space domain (Biondi and Sava, 1999; Shen, 2004). The image-space approach minimizes the residual in the image domain obtained after migration. Regardless of the domain of application, using phase-encoded data can substantially decrease the computational cost of wave-equation tomography(Shen and Symes, 2008; Vigh and Starr, 2008). Tang et al. (2008) extended the theory of image-space wave-equation tomography from the conventional shot-profile domain (Shen, 2004) to the generalized source domain. The generalized source domain can be obtained in two different spaces. In the data-space, shot gathers are combined and the corresponding source function is synthesized, using a convenient phase-encoding scheme, which characterizes the data-space phase encoding (Romero et al., 2000; Whitmore, 1995). In the image-space, source- and receiver-areal data are synthesized by upward propagating wavefields. The initial condition for the modeling is a prestack image computed with wave-equation migration, according to the prestack exploding-reflector modeling (Biondi, 2007,2006). The modeling experiments can be combined such that a small quantity of areal data is generated. In this case, to mitigate crosstalk during imaging, the modeling experiments and reflectors are phase-encoded, characterizing the image-space phase encoding (Guerra and Biondi, 2008). To encode the reflectors, a picking step of some key reflectors is necessary.

In this paper, we show that image-space phase-encoded wavefields can be used to estimate the velocity model in image-space wave-equation tomography. We show that the gradient of the tomographic objective functional is similar to that obtained in the original shot-profile domain, but with less computational cost. Velocity inversion using image-space phase-encoded gathers converges to reasonable results when compared to the correct velocity model, provided that crosstalk has been sufficiently attenuated. We briefly discuss the theory of wave-equation tomography in the image-space domain; then we explain the prestack exploding-reflector modeling and show that the image-space phase encoding can be used to accelerate wave-equation tomography in the image domain. We use the Marmousi model to illustrate the method.

Wave-equation tomography using image-space phase-encoded data